Radicals
write as a mixed radical
sqrt200
10sqrt2
complete the square
f(x)=x^2+4x+9
f(x)=(x+2)^2 +5
what is the equation that can represent the area of a rectangular field that needs to be fenced in with 100m of fencing? (assume you need to fence all 4 sides)
A(x)=x(50-x)
OR
A(x)=x(100-2x)/2
what are the x-intercepts for the function
f(x)=(x+1)(2x-1)
x=-1 and x=1/2
What is the general equation for a quadratic function that has a vertex at (-5,5)?
f(x)=a(x+5)^2 +5
Simplify: write answers as mixed radicals
(3sqrt2)(4sqrt6)-3sqrt3
21sqrt3
Find the vertex of the following function
y=(x+2)(x-4)
(1,-9)
Find two numbers that have a sum of 36 and whose product is a maximum... what is the max product?
the numbers are 18 and 18 and their product is 324!
how many solutions will the quadratic have?
y=8x^2-7x+3
2 solutions! b^2-4ac is greater than 0
What is the general equation of a function that has x-intercepts at 2 and 3?
f(x)=a(x-2)(x-3)
Add the following radicals together
10sqrt2-6sqrt3+6sqrt2+4sqrt3
16sqrt2-2sqrt3
What is the inverse of
f(x)=(x-5)^2-6
f^-1(x)=+-sqrt(x+6)+5
A bag of chips will sell 1000 bags at $3 per bag every week. The chip manufacturers are looking to increase the price of the chips and research has shown that for every $0.10 increase in price, they will sell 10 less bags of chips.
What is a function that could represent the profit for the chips in a week?
f(x)= (1000-10x)(3+0.1x)
If my friend throws a rock with an equation
h(t)=-4.9t^2+10t+1
and I throw another rock with the equation
h(t)=5t+3
Will the two rocks collide? Assume my aim is perfect!
No they will not
what is the equation of the quadratic function that has a vertex at (4,3) and goes through the point (0,-29)?
f(x)=-2(x-4)^2+3
Multiply:
2sqrt3(3sqrt3+4)
18+8sqrt3
Where is the vertex?
f(x)=(x+5)(x+2)
(-3.5, -2.25)
A ball is thrown off a building with the equation h(t)= -4.9t^2+15t+10 . What is the maximum height of the ball (in metres)?
Round to 2 decimal places
The max height is 21.48m
Solve the system of equations
f(x)=3x^2+2x-1
g(x)=3x+1
x=-2/3 and x=1
what is the equation of the quadratic function that has x-intercepts at 1 and -1 and goes through the point (2,18)
f(x)=6(x+1)(x-1)
Simplify this....
(2sqrt5+5sqrt7)(5sqrt5-4sqrt7)
-90+17sqrt35
The rate of change in the surface area of a cell culture can be modelled by the function
S(t)=-0.003(t-5)^2+0.42
where S(t) is the rate of change in the surface area in square millimetres per hours at time t in hours, and 0 ≤ t ≤ 12. Write an equation that relates the time in terms of surface area...
S^-1(t)= +- sqrt(-(t-0.42)/(0.003)) +5
A watch company has been selling 1300 watches per week at $15 each. They are planning a price increase. A survey indicates that for every dollar increase in price, there will be a drop of 50 sales per week. If it costs $10 to make each watch, what should the selling price be to maximize profit and what is the max profit?
Reminder: the profit function is equal to Revenue - Cost
The revenue is the amount of money you sell the watch for multiplied by the number of watches
The cost is the amount it costs to make one watch times the number of watches sold
Maximum Profit happens when there have been 10.5 increases so the cost of the watch is $25.50. The max profit is $12012.50
Profit function is:
P(x)=(1300-50x)(15+x)-(10(1300-50x))
Give the points of intersection
f(x)=3x^2+5x+5
g(x)=x+4
(-1,3) and (-1/3, 11/3)
a quadratic function goes through the points (1,0), (-3,0) and (2,20) what is the equation?
f(x)=4(x-1)(x+3)